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A high-order discontinuous Galerkin method with unstructured space–time meshes for two-dimensional compressible flows on domains with large deformations
We introduce a high-order accurate space-time discontinuous Galerkin method for solving two-dimensional compressible flow problems on fully unstructured space-time meshes. The discretization is based on a nodal formulation, with appropriate numerical fluxes for the first and the second-order terms, respectively. The scheme is implicit, and we solve the resulting non-linear systems using a parallel Newton-Krylov solver. The meshes are produced by a mesh moving technique with element connectivity updates, and the corresponding space-time elements are produced directly based on these local operations. To obtain globally conforming tetrahedral meshes, we first derive the required conditions on a prism boundary mesh to allow for a valid local triangulation. Next, we present an efficient algorithm for finding a global mesh that satisfies these conditions. We additionally show how to add and remove mesh nodes, again using local constructs for the space-time mesh. Our approach is demonstrated on a number of test problems, showing the high-order accuracy for model problems, and the ability to solve flow problems on domains with complex large deformations.
An assessment of atypical mesh topologies for low-Mach large-eddy simulation
An implicit, low-dissipation, low-Mach, variable density control volume finite element formulation is used to explore foundational understanding of numerical accuracy for large-eddy simulation applications on hybrid meshes. Detailed simulation comparisons are made between low-order hexahedral, tetrahedral, pyramid, and wedge/prism topologies against a third-order, unstructured hexahedral topology. Using smooth analytical and manufactured low-Mach solutions, design-order convergence is established for the hexahedral, tetrahedral, pyramid, and wedge element topologies using a new open boundary condition based on energy-stable methodologies previously deployed within a finite-difference context. A wide range of simulations demonstrate that low-order hexahedral- and wedge-based element topologies behave nearly identically in both computed numerical errors and overall simulation timings. Moreover, low-order tetrahedral and pyramid element topologies also display nearly the same numerical characteristics. Although the superiority of the hexahedral-based topology is clearly demonstrated for trivial laminar, principally-aligned flows, e.g., a 1x2x10 channel flow with specified pressure drop, this advantage is reduced for non-aligned, turbulent flows including the Taylor–Green Vortex, turbulent plane channel flow ( Re τ 395), and buoyant flow past a heated cylinder. With the order of accuracy demonstrated for both homogenous and hybrid meshes, it is shown that solution verification for the selected complex flows can be established for all topology types. Although the number of elements in a mesh of like spacing comprised of tetrahedral, wedge, or pyramid elements increases as compared to the hexahedral counterpart, for wall-resolved large-eddy simulation, the increased assembly and residual evaluation computational time for non-hexahedral is offset by more efficient linear solver times. Lastly, most simulation results indicate that modest polynomial promotion provides a significant increase in solution accuracy.
Effect of the numerical discretization scheme in Shock-Driven turbulent mixing simulations
In this work, we evaluate the effects of distinct numerical strategies in simulations of shock-driven turbulent mixing. An air-SF 6 -air gas curtain subjected to Mach 1.2 shock-waves is computed with Implicit Large-Eddy Simulation based on three numerical schemes: directional-split with Harten-Lax-van Leer (HLL) solver; directional-unsplit using HLL-Contact (HLLC) solver; and directional-unsplit with HLLC solver and a Low Mach number Correction (LMC). The results illustrate the importance of the numerical strategy to the accuracy of the predictions. Whereas both split and unsplit schemes result in a similar spatial development of the initial shock-driven instability, only the unsplit schemes can predict the turbulent mixing transition after reshock observed by the laboratory experiments. Such feature increases the mixing rate of the two fluids, this being particularly pronounced when the LMC is active due to i) the reduced flow Mach number, and ii) the larger effective Reynolds number. Since the selected mixing problem is driven by the deposition of vorticity at the fluids’ interface, the resultant flow physics is analyzed by investigating the contribution of distinct inviscid mechanisms to the production of vorticity: baroclinicity, stretching, and dilatation. As expected, it is observed that the production of vorticity is initially dominated by the baroclinicity mechanism. Yet, the relevance of the remainder mechanisms is enhanced after the reshock and may even surpass the baroclinicity term.
On the use of a multigrid-reduction-in-time algorithm for multiscale convergence of turbulence simulations
Simulations of turbulent flow present challenges in terms of accuracy and affordability on modern highly-parallel computer architectures. A multigrid-reduction-in-time algorithm is used to provide a framework for separately evolving different scales of turbulence and for parallelizing the temporal domain, thereby increasing the concurrency. It is hypothesized that the space–time locality of the small scales of turbulence can be used to circumvent difficulties in applying temporal multigrid to flows dominated by inertial physics. For algorithms that fall well short of spectral accuracy (fourth-order is used in this work) attention must be paid to the accuracy of features on scales transferred between multigrid levels. Numerical experiments were performed using implicit large-eddy simulation. Results from applying the approach to an infinite-Reynolds number Taylor–Green flow and a double-shear flow at a Reynolds number of 11650 provide strong evidence that the approach has merit. The multigrid-reduction-in-time framework can be used to parallelize the temporal domain of a high-Reynolds-number turbulent flow and permit independent convergence of different scales. Establishing this foundation allows for future research in reducing the wall-clock time to solve turbulent flows while retaining the same accuracy as sequential solvers. In conclusion, current performance results from parallelizing the temporal domain are not competitive with those from sequential-in-time methods.
On Eliminating Synchronous Communication in Molecular Simulations to Improve Scalability
Molecular dynamics simulation, as a complementary tool to experimentation, has become an important methodology for the understanding and design of molecular systems as it provides access to properties that are difficult, impossible or prohibitively expensive to obtain experimentally. Many of the available software packages have been parallelized to take advantage of modern massively concurrent processing resources. The challenge in achieving parallel efficiency is commonly attributed to the fact that molecular dynamics algorithms are communication intensive. This paper illustrates how an appropriately chosen data distribution and asynchronous one-sided communication approach can be used to effectively deal with the data movement within the Global Arrays/ARMCI programming model framework. A new put_notify capability is presented here, allowing the implementation of the molecular dynamics algorithm without any explicit global or local synchronization or global data reduction operations. In addition, this push-data model is shown to very effectively allow hiding data communication behind computation. Rather than data movement or explicit global reductions, the implicit synchronization of the algorithm becomes the primary challenge for scalability. Without any explicit synchronous operations, the scalability of molecular simulations is shown to depend only on the ability to evenly balance computational load.
Scalable Metropolis Monte Carlo for simulation of hard shapes
We design and implement a scalable hard particle Monte Carlo simulation toolkit (HPMC), and release it open source as part of HOOMD-blue. HPMC runs in parallel on many CPUs and many GPUs using domain decomposition. We employ BVH trees instead of cell lists on the CPU for fast performance, especially with large particle size disparity, and optimize inner loops with SIMD vector intrinsics on the CPU. Our GPU kernel proposes many trial moves in parallel on a checkerboard and uses a block-level queue to redistribute work among threads and avoid divergence. HPMC supports a wide variety of shape classes, including spheres/disks, unions of spheres, convex polygons, convex spheropolygons, concave polygons, ellipsoids/ellipses, convex polyhedra, convex spheropolyhedra, spheres cut by planes, and concave polyhedra. NVT and NPT ensembles can be run in 2D or 3D triclinic boxes. Additional integration schemes permit Frenkel–Ladd free energy computations and implicit depletant simulations. In a benchmark system of a fluid of 4096 pentagons, HPMC performs 10 million sweeps in 10 min on 96 CPU cores on XSEDE Comet. The same simulation would take 7.6 h in serial. HPMC also scales to large system sizes, and the same benchmark with 16.8 million particles runs in 1.4 h on 2048 GPUs on OLCF Titan.
Aspherical particle models for molecular dynamics simulation
In traditional molecular dynamics (MD) simulations, atoms and coarse-grained particles are modeled as point masses interacting via isotropic potentials. For studies where particle shape plays a vital role, more complex models are required. Here, we describe a spectrum of approaches for modeling aspherical particles, all of which are now available (some recently) as options within the LAMMPS MD package. Broadly these include two classes of models. In the first, individual particles are aspherical, either via a pairwise anisotropic potential which implicitly assigns a simple geometric shape to each particle, or in a more general way where particles store internal state which can explicitly define a complex geometric shape. In the second class of models, individual particles are simple points or spheres, but rigid body constraints are used to create composite aspherical particles in a variety of complex shapes. This work discusses parallel algorithms and associated data structures for both kinds of models, which enable dynamics simulations of aspherical particle systems across a wide range of length and time scales. We also highlight parallel performance and scalability and give a few illustrative examples of aspherical models in different contexts.
Linear and nonlinear benchmarks between the CLT code and the M3D-C1 code for the 2/1 resistive tearing mode and the 1/1 resistive kink mode
Here, the linear and nonlinear benchmarks between the CLT code and the M3D-C1 code for the 2/1 resistive tearing mode and the 1/1 resistive kink mode are presented. CLT is an explicit finite difference code, while M3D-C1 is an implicit finite element code. Although the implementations of CLT and M3D-C1 are totally different, we find that the simulation results of the resistive-kink mode and the m/n=2/1 tearing mode from M3D-C1 and CLT are almost the same, including the linear and nonlinear growth rates, the mode structures, the nonlinear saturation levels, the Poincare plots, and the scaling laws. This confirms that the nonlinear results for the 1/1 resistive-kink mode and 2/1 tearing mode are accurate and reliable.
Quasi-Helmholtz decomposition, Gauss' laws and charge conservation for finite element particle-in-cell
Development of particle-in-cell (PIC) methods using finite element based methods (FEMs) have been a topic of renewed interest; this has largely been driven by (a) the ability of finite element methods to better model geometry, (b) better understanding of function spaces that are necessary to represent all Maxwell quantities, and (c) more recently, the fundamental rubrics that should be obeyed in space and time so as to satisfy Gauss' laws and the equation of continuity. In that vein, methods have been developed recently that satisfy these equations and are agnostic to time stepping methods. While this development is indeed a significant advance, it should be noted that implicit FEM transient solvers support an underlying null space that corresponds to a gradient of a scalar potential ∇Φ(r) (or t∇Φ(r) in the case of wave equation solvers). While explicit schemes do not suffer from this drawback, they are only conditionally stable with time step sizes that are mesh dependent and very small. Furthermore, the null space produces spurious charge that can corrupt the desired physics of a PIC simulation. The way to overcome this bottleneck, and indeed, satisfy all four Maxwell's equation is to use a quasi-Helmholtz formulation on a tessellation. In the re-formulation presented, we strictly satisfy the equation of continuity and Gauss' laws for both the electric and magnetic flux densities. Results illustrating the efficacy of this scheme will be demonstrated by analyzing non-neutral beams with space-charge and the adiabatic expansion of a neutral plasma with realistic parameters (Debye length and real mass ratios).
Multi-center semi-empirical quantum models for carbon under extreme thermodynamic conditions
We report on the development of many-body density functional tight binding (DFTB) models for carbon, which include either explicit or implicit calculation of multi-center terms in the Hamiltonian. Here, we show that all of our methods yield accurate eigenstates and eigenfunctions for both ambient diamond and transitions to molten, metallic states. We then determine a three-body repulsive energy to compute accurate equation of state and structural properties for carbon under these conditions. Our results indicate a straightforward approach by which many-body effects can be included in DFTB, thus extending the method to a wide variety of systems and thermodynamic conditions.
Cross-scale modeling of storm surge, tide, and inundation in Mid-Atlantic Bight and New York City during Hurricane Sandy, 2012
Driven by high-resolution NAM (North America Mesoscale) and ECMWF (European Centre for Medium-Range Weather Forecasts) atmospheric fields, a 3-D unstructured grid SCHISM (Semi-implicit Cross-scale Hydroscience Integrated System Model) was applied to simulate total water level in the Mid-Atlantic Bight during Hurricane Sandy in 2012. The simulated storm surge, tide, significant wave height, and wave peak period results compared favorably with NOAA observations along US East Coast, Long Island Sound, and New York Harbor. The maximum total water level at The Battery in the New York Harbor was accurately simulated with an absolute error of less than 0.08 m (out of 2.9 m peak surge) and a timing difference less than 10 min, which includes the effects on the order of 0.1–0.3 m (5–10%) from the coastal setup induced by the surface waves. The scenario comparisons of (1) “NAM” versus “ECMWF”, (2) “2-D” versus “3-D”, and (3) “with” versus “without” wind wave model were examined. The 3-D barotropic model forced by ECMWF including the effects of wind waves performs the best, attributed to wave-induced radiation stress and reduction of bottom stress when the 3-D version is used. Simultaneously, the ELCIRC-Sub model, using a 5-m topography/bathymetry sub-grid and a regular 200-m resolution finite volume computational model grid, was developed to simulate the street-level inundation in New York City. The momentum and mass fluxes calculated by the coarser base grid model were effectively coupled with the sub-grid so that running a full-blown high-resolution base model is not required. The ELCIRC-Sub model uses MPI (Message Passing Interface) parallel computing to enlarge the coverage of the land surface and an efficient non-linear solver to improve the accuracy of the wetting-and-drying processes. The temporal comparisons of modeled water level with NOAA's tidal stations and USGS' rapid-deployed gauges showed overall performance with an average error of 0.1 m. Particularly, ELCIRC-Sub captured the profile of the highest peak surge (3.9 m), which rose 2 m within 3 hour at Kings Point, NY. The spatial comparisons of the modeled peak water level at 80 surveyed locations showed an average error less than 0.13 m. The modeled maximum inundation extent also matched well with an 80% hit rate against FEMA's Hurricane Sandy maximum flooding extent.
Effects of Asperity Distribution on Fluid Flow and Induced Seismicity During Deep Geothermal Exploitation
This work investigates the injection-induced seismic response of a heterogeneous fault plane, featuring low-permeability asperities embedded into a high-permeability damage zone. We simulate the pressure evolution with a hydrogeological simulator, accounting for the heterogeneous fault plane. Seismicity occurs then on the asperities, represented as unstable patches reactivating by means of the Mohr-Coulomb criterion. The hydrological and seismic modules are implicitly coupled to account for effects of asperity reactivation on the permeability. Results show that permeability changes may cause at a later time a change in seismicity propagation. Finally, we also investigated such effects by varying the density of asperities.
Strategy making and power in environmental assessments. Lessons from the establishment of an out-of-town shopping centre in Vaesteras, Sweden
This paper seeks to provide deeper insights into how EA ineffectiveness is produced in land use planning practice. This is explored in a study of local development planning in the city of Vaesteras, Sweden. The case in question is the development of a large out-of-town shopping centre, propelled by the establishment of a new IKEA furniture store. The Healey (2007) framework of planning as strategy making is applied as an analytical framework, together with a focus on power-knowledge relations. In the analysis, we identify a range of mechanisms that produced ineffectiveness by limiting the role of environmental knowledge throughout the planning process. The specific mechanisms we identified were related to the overall consensus perspective in local development strategies and plans, a lack of concretisation and integration of various policies and strategies, a range of exclusion mechanisms and an overall focus on mitigation and benefits of the process in question. In practice, these mechanisms were closely intertwined. Our main conclusion is, consequently, that increased effectiveness of EA would require fundamental transformation of the norms, frameworks and routines that implicitly and explicitly guide land use planning in practice. - Highlights: Black-Right-Pointing-Pointer We analyse how EA-ineffectiveness is produced in land use planning practice. Black-Right-Pointing-Pointer Several mechanisms produce EA-ineffectiveness throughout the whole planning process. Black-Right-Pointing-Pointer These mechanisms are often closely intertwined and mutually reinforcing each other. Black-Right-Pointing-Pointer Enhancing EA-effectiveness requires a fundamental shift of the norms, frameworks and routines shaping planning practice.
Index-based groundwater vulnerability mapping models using hydrogeological settings: A critical evaluation
Groundwater vulnerability maps are useful for decision making in land use planning and water resource management. This paper reviews the various groundwater vulnerability assessment models developed across the world. Each model has been evaluated in terms of its pros and cons and the environmental conditions of its application. The paper further discusses the validation techniques used for the generated vulnerability maps by various models. Implicit challenges associated with the development of the groundwater vulnerability assessment models have also been identified with scientific considerations to the parameter relations and their selections. - Highlights: • Various index-based groundwater vulnerability assessment models have been discussed. • A comparative analysis of the models and its applicability in different hydrogeological settings has been discussed. • Research problems of underlying vulnerability assessment models are also reported in this review paper.
Cumulative effects in strategic environmental assessment: The influence of plan boundaries
Cumulative effects (CE) assessment is lacking quality in impact assessment (IA) worldwide. It has been argued that the strategic environmental assessment (SEA) provides a suitable IA framework for addressing CE because it is applied to developments with broad boundaries, but few have tested this claim. Through a case study on the Danish mining sector, this article explores how plan boundaries influence the analytical boundaries applied for assessing CE in SEA. The case was studied through document analysis in combination with semi-structured group interviews of the responsible planners, who also serve as SEA practitioners. It was found that CE are to some extent assessed and managed implicitly throughout the planning process. However, this is through a focus on lowering the cumulative stress of mining rather than the cumulative stress on and capacity of the receiving environment. Plan boundaries do influence CE assessment, though all boundaries are not equally influential. The geographical and time boundaries of the Danish mining plans are broad or flexible enough to accommodate a meaningful assessment of CE, but the topical boundary is restrictive. The study indicates that collaboration among planning authorities and legally appointed CE leadership may facilitate better practice on CE assessment in sector-specific SEA contexts. However, most pressing is the need for relating assessment to the receiving environment as opposed to solely the stress of a proposed plan.
Scheduling double round-robin tournaments with divisional play using constraint programming
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